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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Geometry and Topology Seminar: The prescribed Weingarten curvatures problem in hyperbolic space

Presented by Daniel Ballesteros-Chavez, Durham

18 January 2018 13:00 in CM221

We will present a detailed proof for the existence of a closed convex hypersurface in the hyperbolic ball with prescribed 1 \le k < n - Weingarten curvature. Specifically, we deal with the equivariant problem for a sufficiently large group of hyperbolic automorhphisms. The proof proceeds by establishing (nonlinear) strict ellipticity of the associated PDE. Then we obtain existence in C^{1,a} for an auxiliary problem by Schauder theory, C^2 smoothness using ellipticity and a Lemma by Cheng-Yau, and C^{2,a} - regularity by Evans-Krylov. Finally, existence of a solution is established by degree theory in the equivariant setting. The results presented are part of the speakers PhD thesis.

Contact mark.a.powell@durham.ac.uk or andrew.lobb@durham.ac.uk or wilhelm.klingenberg@durham.ac.uk for more information